A railcar re-blocking strategy via Mixed Integer Quadratic Programming

This article presents a novel solution namely Pre-blocking through Re-waybilling to minimize railcar cuts in freight railways. The Pre-blocking through Re-waybilling Problem (PRP) can be described as follows: A freight train carrying m railcars, loaded or empty, arrives at a local classification yard where, based on the destination on their electronic waybills, railcars will be physically switched to n outbound trains. Number of railcar cuts depends on the order of railcars on train. The objective is to minimize the number of railcar cuts by means of changing the electronic waybills of empty railcars, i.e. re-assignment of empty railcars to customers, while respecting supply, demand, and feasibility constraints. In order to solve this problem, a supply–demand network is constructed first, where supply nodes and demand nodes represent railcars and destinations, respectively. The problem is then formulated as a modified transportation problem. Unlike the conventional transportation problem, a linear arc cost function is proposed to describe the adjacent cars’ impact on railcar cut. The objective is converted to a quadratic function, leading to a Mixed-Integer Quadratic Programming (MIQP) problem. We improve proposed MIQP to a Convex Mixed-Integer Quadratic Programming (C-MIQP) problem by adding a quadratic term to the objective function. Illustrative and realistic examples are presented to validate the feasibility and efficiency of proposed pre-blocking optimizer.